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Exactly
Interesting... You thought of the 365.25 days per year

Of course ! They've taught me well.

EEK ! I just noticed I accidentally wrote "(acceleration = velocity * time)" .. when of course it should say "(velocity = acceleration * time)" .. my formula was correct, after all; just not the description.

By the way ...
My age is the only number (aside from zero) that equals twice the sum of its digits (in base ten ).

Okay, so...
10a+b is your age
2a+2b=10a+b
I guess you are younger than 100 years, or else the equation would have more than two solutions, I think.
<=> b=8a AND b<10 because a and be are only digits.
So a can't be greater than 1
a=1, b=8; I am older than you

True.

But proving it to be the only solution may be a more difficult feat.

Why? a and b are both digits. And then you can just test them: a=0 -> b=0; a=1 -> b=1, a>2 -> b>16, so b isn't a digit anymore. (> means "greater or equal" here). Not too difficult I'd say^^

Oh, and if you were more than 99 years old, it would be 100a+10b+c=2a+2b+2c. 2a+2b+2c cannot be greater than 2*9+2*9+2*9=54, so a must be 0 because for a>1, you would end up far above 54.

im staying out this one i dont know physics

Of course not, if you are 12 It is all a matter of age

my age is 2 more than the sum of all X and Y for the first three pairs (x,y) which satisfy the equation

x^2 + 7 = 2^y while still being positive integers.

dammit i was looking at the wrong numbers, make that

the sum of the three differences, between the first four x,y

let me explain. :p

1. (x1,y1) satisfy the equation
2. (x2,y2) satisfy the equation
3. (x3,y3) satisfy the equation
4. (x4,y4) satisfy the equation

(x2-x1) + (x3-x2) + (x4-x3) + (y2-y1) + (y3-y2) + (y4-y3)

is 2 less than my age